Answer:
[tex]2\sqrt{55}\text{ m/s or }\approx 14.8\text{m/s}[/tex]
Step-by-step explanation:
The vertical component of the initial launch can be found using basic trigonometry. In any right triangle, the sine of an angle is equal to its opposite side divided by the hypotenuse. Let the vertical component at launch be [tex]y[/tex]. The magnitude of [tex]40\text{ m/s}[/tex] will be the hypotenuse, and the relevant angle is the angle to the horizontal at launch. Since we're given that the angle of elevation is [tex]60^{\circ}[/tex], we have:
[tex]\sin 60^{\circ}=\frac{y}{40},\\y=40\sin 60^{\circ},\\y=20\sqrt{3}[/tex](Recall that [tex]\sin 60^{\circ}=\frac{\sqrt{3}}{2}[/tex])
Now that we've found the vertical component of the velocity and launch, we can use kinematics equation [tex]v_f^2=v_i^2+2a\Delta y[/tex] to solve this problem, where [tex]v_f/v_i[/tex] is final and initial velocity, respectively, [tex]a[/tex] is acceleration, and [tex]\Delta y[/tex] is distance travelled. The only acceleration is acceleration due to gravity, which is approximately [tex]9.8\:\mathrm{m/s^2}[/tex]. However, since the projectile is moving up and gravity is pulling down, acceleration should be negative, represent the direction of the acceleration.
What we know:
[tex]v_i=20\sqrt{3}\text{ m/s}[/tex] [tex]a=-9.8\:\mathrm{m/s^2}[/tex] [tex]\Delta y =50\text{ m}[/tex]Solving for [tex]v_f[/tex]:
[tex]v_f^2=(20\sqrt{3})^2+2(-9.8)(50),\\v_f^2=1200-980,\\v_f^2=220,\\v_f=\sqrt{220}=\boxed{2\sqrt{55}\text{ m/s}}[/tex]
need help w this question thanksss!
Given:
A figure of a circle.
To find:
The value of x.
Solution:
Central angle theorem: According to this theorem, the central angle on an arc is twice of the subtended angle on that arc.
Using the central angle theorem, we get
[tex]x=2\times 35^\circ[/tex]
[tex]x=70^\circ[/tex]
Therefore, the value of x is 70 degrees.
GIVE AN EXPLANATION PLEASE! A BRAINLEEST IF TWO OR MORE PEOPLE HAVE ANSWERED IT. (FIRST COME FIRST SERVE BASES + ANSWER HAS TO BE CORRECT)
Lily bought a pair of gloves and a shirt.
The gloves cost £4
She sold the gloves and the shirt for a total of £48
She made 100% profit on the cost of the gloves.
20% profit on the total cost.
Work out her percentage profit on the cost of the skirt.
Answer 1 decimal place.
The profit percentage = 16.3%
what is the equation of the circle shown in the graph?
Answer:
(x + 6)² + (y - 4)² = 9
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Here (h, k ) = (- 6, 4 ) and r = 3 , then
(x - (- 6) )² + (y - 4)² = 3² , that is
(x + 6)² + (y - 4)² = 9
2 points The compound interest on a certain sum for the first year for 4 % is Rs. 25. The compound interest for 2 years at the same rate on the same sum will be ...
Answer:
The interest for the two years is Rs 51.
Step-by-step explanation:
Rate, R = 4 %
Compound interest for 1 year = Rs 25
Let the sum is P.
For first year,
[tex]A = P \left ( 1+\frac{R}{100} \right )^1\\\\A = P(1+0.04)\\\\A - P = 0.04 P\\\\0.04 P = 25\\\\P= Rs625[/tex]
For 2 year
[tex]A = P \left ( 1+\frac{R}{100} \right )^2\\\\A = 625(1+0.04)^2\\\\A = 676\\[/tex]
Interest is
Interest = Rs 676 - Rs 625 = Rs 51
The height of a cone is two times its base diameter. What is the volume of the cone in terms of its base radius r?
options are on the picture:)
Answer:-
The option B is the right answer.
Solution:-
[tex] \sf h = 2d = 2 \: • \: 2r = 4r[/tex]
[tex] \sf = \frac{1}{3} \pi {r}^{2} h[/tex]
[tex] \sf = \frac{1}{3} \pi {r}^{2} \: • \: 4r[/tex]
[tex] \sf = \frac{4}{3} \pi {r}^{3} \: \green✓ [/tex]
When the angle of elevation of the sun is
42°, fnd the length of the shadow, to the
nearest foot, cast by a tree 60 feet tall.
Answer:
The shadow length is 67
Step-by-step explanation:
solution shown in the picture
Small Manufacturing Company has a standard overhead rate of $42 per hour. The labor rate is $20 per hour. Overhead is applied based on direct labor hours. Jobs B-1 and B-2 were completed during the month of March. Small incurred 140 hours of indirect labor during the month
The question is incomplete. The complete question is :
Small Manufacturing Company has a standard overhead rate of $42 per hour. The labor rate is $15 per hour. Overhead is applied based on direct labor hours. Jobs B-1 and B-2 were completed during the month of March. Small incurred 140 hours of indirect labor during the month. Job B-1 used 82 direct labor hours and $3650 worth of direct material used. Job B-2 used 130 direct labor hours and $2,900 worth of direct material. What is the total cost of job B-2? Round to closest whole dollar (no cents).
Solution :
Particulars Job B-2
Direct material used $ 2,900
Add : Direct labor cost (130 hours x $15) $ 1,950
Add : overhead cost (130 hours x $ 42) $ 5,460
Total Cost of Job B-2 $ 10,310
Therefore, the total cost of the Job B-2 is $ 10,310.
If f(x)=3x^(2)+1 and G(x)=2x-3 what would f(f(x))
Answer:
f(f(x)) = 27[tex]x^{4}[/tex] + 18x² + 4
Step-by-step explanation:
To find f(f(x)) substitute x = f(x) into f(x) , that is
f(3x² + 1)
= 3(3x² + 1)² + 1 ← expand parenthesis using FOIL
= 3(9[tex]x^{4}[/tex] + 6x² + 1) + 1 ← distribute parenthesis by 3
= 27[tex]x^{4}[/tex] + 18x² + 3 + 1 ← collect like terms
= 27[tex]x^{4}[/tex] + 18x² + 4
Hello,
[tex](fof)(x)=f(f(x))\\\\=3(3x^2+1)^2+1\\\\=3(9x^4+6x^2+1)+1\\\\\boxed{=27x^4+18x^2+4}[/tex]
I need help with my math!!!
Answer:
The correct answer is y = | x + 6 |
instructions: state what additional information is required in order to know that the triangle in the image below are congruent for the reason given.
Given: AAS
Answer:
QP ≈ HG
Common side between those angles are QP and HG
so, they should be congruent to prove AAS
Answered by GAUTHMATH
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Mount Everest, at 29,028 feet, is the tallest mountain on the Earth. What is its height in kilometers
Answer:
8.8477344 km
Step-by-step explanation:
[tex] \because \: 1 \: ft = 0.000305 \: kilometre \\ \\ \therefore \: 29028 \: ft = 29028 \times 0.000305 \: km \\ \\ = 8.8477344 \: km[/tex]
Please help me with this, no clue.
What is the multiplicative rate of change for the exponential function f(x) = 21
2
(sqrt)48,400 is a number that lies
between which two powers of 10?
Answer:4 and 8?
Step-by-step explanation:
Select the instances in which the variable described is binomial.1) A coin flip has two outcomes: heads or tails. The probability of each outcome is 0.50. The random variable represents the total number of flips required to get tails.2) A quality check on a particular product must meet five guidelines. All products are made in the same factory under the same conditions. The random variable represents the total number of products out of 35 tested that pass inspection.3) There are two choices of burritos at a restaurant, vegetarian or beef. The random variable represents the total number out of 254 customers who ordered beef.4) Based on the parents' genetics, each of 6 children from a particular pair of parents has a 0.30 probability of having blue eyes. The random variable represents the total number of children from this pair of parents with blue eyes.5) The probability of drawing a king in a standard deck of cards is 0.08. Seven cards are drawn without replacement. The random variable represents the total number of king cards observed.
Answer: 2) A quality check on a particular product must meet five guidelines. All products are made in the same factory under the same conditions. The random variable represents the total number of products out of 35 tested that pass inspection.
• 3) There are two choices of burritos at a restaurant, vegetarian or beef. The random variable represents the total number out of 254 customers who ordered beef.
• 4) Based on the parents' genetics, each of 6 children from a particular pair of parents has a 0.30 probability of having blue eyes. The random variable represents the total number of children from this pair of parents with blue eyes
Step-by-step explanation:
The binomial distribution simply means the probability of success or failure in an experiment. The instances in which the variable described is binomial are given below:
• 2) A quality check on a particular product must meet five guidelines. All products are made in the same factory under the same conditions. The random variable represents the total number of products out of 35 tested that pass inspection.
• 3) There are two choices of burritos at a restaurant, vegetarian or beef. The random variable represents the total number out of 254 customers who ordered beef.
• 4) Based on the parents' genetics, each of 6 children from a particular pair of parents has a 0.30 probability of having blue eyes. The random variable represents the total number of children from this pair of parents with blue eyes.
Option 1 isn't binomial since the number of trails that are given isn't fixed. Option 5 isn't binomial as well
Therefore, the correct options are 2,3 and 4.
Please help me this is due in like five minutes
Answer:
20 cm²
Step-by-step explanation:
Area of the square = 2cm * 2cm = 4 cm²
Area of All triangles = (4cm * 2cm) ÷ 2cm * 4cm = (4cm * 2cm) * 2cm = 16 cm²
Total Area = 4 cm² + 16 cm² = 20 cm²
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
2m^2-5m-3=0 by factorization
Answer:
M= 6, -1
Step-by-step explanation:
Factoring these numbers, it will result in (m-6)(m+1). So, m= 6,-1
If the point ((4,-2) what is included in a direct viration relationship which point also belongs and variation
Answer:
The answer is "This direct variant (-4,2) is part of it".
Step-by-step explanation:
The equation expresses its direct variation relation
[tex]y = mx ........ (1)[/tex]
Where x and y vary directly, and k vary continuously.
Now so the point (4,-2) is in the direct relation of variation, so from equation (1) we are given,[tex]-2 = 4m[/tex]
[tex]\to m=-\frac{1}{2}[/tex]
The equation (1) is therefore converted into
[tex]\to y=-\frac{1}{2}x \\\\\to x + 2y = 0 ......... (2)[/tex]
Then only the point (-4,2) satisfies the connection with the four possibilities (2). Therefore (-4,2) is a direct variant of this.
f(x) = square root 32x
g(x) = square root 2x
Given:
The two functions are:
[tex]f(x)=\sqrt{32x}[/tex]
[tex]g(x)=\sqrt{2x}[/tex]
To find:
The [tex](f\cdot g)(x)[/tex]. Assume [tex]x\geq 0[/tex].
Solution:
We have,
[tex]f(x)=\sqrt{32x}[/tex]
[tex]g(x)=\sqrt{2x}[/tex]
Now,
[tex](f\cdot g)(x)=f(x)\cdot g(x)[/tex]
[tex](f\cdot g)(x)=\sqrt{32x}\cdot \sqrt{2x}[/tex]
[tex](f\cdot g)(x)=\sqrt{32x\times 2x}[/tex]
[tex](f\cdot g)(x)=\sqrt{64x^2}[/tex]
[tex](f\cdot g)(x)=8x[/tex]
Therefore, the correct option is A.
What are the minimum and maximum distances that Morgan’s dog may be from the house? (Algebra ll) *URGENT*
Given:
The minimum and maximum distance that the dog may be from the house can be found by using the equation:
[tex]|x-500|=8[/tex]
To find:
The minimum and maximum distance that the dog may be from the house.
Solution:
We have,
[tex]|x-500|=8[/tex]
It can be written as:
[tex]x-500=\pm 8[/tex]
Adding 500 on both sides, we get
[tex]x=500\pm 8[/tex]
Now,
[tex]x=500+8[/tex] and [tex]x=500-8[/tex]
[tex]x=508[/tex] and [tex]x=492[/tex]
The minimum distance is 492 meters and the maximum distance is 508 meters.
Therefore, the correct option is C.
Find the roots of the equation x^2 + 16 = 0.
Answer:
+4 and -4
Step-by-step explanation:
x² + 16=0
x=-√16
x=-4 or +4
If < A and < B are vertical angles, and < A is 43 ° , then what is the measure of < B?
Select one:
a. 47 °
b. 137 °
c. 21 °
d. 43 °
Answer:
d
Step-by-step explanation:
vertical angles are congruent , so
∠ B = ∠ A = 43°
A sea turtle can swim 13 kilometers in 5 hours at this rate speed how far can it travel in 9 hours
Answer:
23.4 km
Step-by-step explanation:
We can use a ratio to solve
13 km x km
-------- = ---------------
5 hours 9 hours
Using cross products
13*9 = 5x
117 = 5x
Divide each side by 5
117/5 = 5x/5
23.4 =x
Answer:
It travel 23.4 km in 9 hours.
Step-by-step explanation:
Given :-
A sea turtle can swim 13 km in 5 hours at this rate speed .
To find :-
How far can it travel in 9 hours.
Solution :-
Sea turtle swim 13 km in 5 hours Then find the how far it can travel in 9 hours.
Let us assume that In 9 hours turtle swim x km.
Now, We solve by using ratio for x.
In 5 hours it swim = 13 km
And, In 9 hours it swim = x km
Calculate for x
5 hours = 13 km
9 hours = x km
Use cross multiplication method , we get
5 × x = 9 × 13
5x = 117
Divide both side by 5
5x / 5 = 117 / 5
x = 23.4
Hence, It can travel 23.4 km in 9 hours.
represent the following additions on a number line 3+5=8 3+(-5)
Answer:
8 &-2
Step-by-step explanation:
<-------------------------->
-2-1 0 1 2 3 4 5 6 7 8
________________
-2<8 and 8>-2
Find the surface area of the
triangular prism.
7 cm
cm
7 cm
9 cm
5 cm
[?] sq cm
Please HELP ME
Hello,
I am going to calculate all the surface areas of the prism:
1) the bases: 2*(6*9)/2=64 (cm²)
2) perimeter of the base: 7+9+7=23 (cm)
3 lateral area: 23*5=115 (cm²)
All surface areas= 64+115=179 (cm²)
What does it means sq ? (for a foreigner) ?
All surface areas= 64+115=179 (cm²)
What is triangular prisms?A three-sided polyhedron consisting of a triangle base, a translated copy, and three faces connecting equivalent sides is known as a triangular prism in geometry. If the sides of a right triangular prism are not rectangular, the prism is oblique.
Given
the bases: 2*(6*9)/2=64 (cm²)
perimeter of the base: 7+9+7=23 (cm)
3 lateral area: 23*5=115 (cm²)
All surface areas= 64+115=179 (cm²)
To know more about triangular prisms refer to:
https://brainly.com/question/3160908
#SPJ2
Mary ran 2 miles in about 23 minutes If she continued at the same pace how long will it take her to run 10 miles?
What is the inverse of the function f(x)
-x + 2?
q
O h(x) = 18x - 2
h(x) = 9x - 18
O h(x) = 9x + 18
® h(x) - 18x + 2
Answer:
[tex]h(x)= 9x - 18[/tex]
Step-by-step explanation:
Given
[tex]f(x) = \frac{1}{9}x + 2[/tex]
Required
The inverse
[tex]f(x) = \frac{1}{9}x + 2[/tex]
Replace f(x) with y
[tex]y = \frac{1}{9}x + 2[/tex]
Swap x and y
[tex]x = \frac{1}{9}y + 2[/tex]
Subtract 2
[tex]x - 2= \frac{1}{9}y[/tex]
Multiply 9
[tex]9x - 18 = y[/tex]
Rewrite as:
[tex]y = 9x - 18[/tex]
So:
[tex]h(x)= 9x - 18[/tex]
Which congruence theorem can be used to prove BDAS DBC?
Answer:
We know that the hypotenuse-leg theorem states that if the hypotenuse and one leg of a right triangle are congruent to hypotenuse and corresponding leg of another right triangle, then the triangles are congruent. hypotenuse(AB) of △BDA equals to hypotenuse (CD) of △DBC.
Answer:
A. HL
Step-by-step explanation:
2
What is the value of x in the equation 7x + 2y = 48, when y = 3?
Answer: 6
Step-by-step explanation: 7x+2y=48
7x+2(3)=48
7x+6=48
7x=48+6
7x=42
x=42/7
x=6