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3 years ago

What is the length of the hypotenuse

Mathematics

2 answers:

Afina-wow [57]3 years ago

8 0

Answer:

Its C

If u didn't feel like reading.

Step-by-step explanation:

nika2105 [10]3 years ago

5 0

Given:

Given that the length of the two legs of the right triangle are 28 m and 45 m.

We need to determine the length of the hypotenuse.

Length of the hypotenuse:

The length of the hypotenuse can be determined using the Pythagorean theorem.

Thus, we have;

$hyp^2=28^2+45^2$

Simplifying, we get;

$hyp^2=784+2025$

$hyp^2=2809$

Taking square root on both sides, we get;

$hyp=\sqrt{2809}$

$hyp=53 \ m$

Thus, the length of the hypotenuse is 53 m

Hence, Option C is the correct answer.

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A 25ft ladder is placed 7 feet from the wall, as shown. How high up the wall with the ladder reach?

ss7ja [257]

Answer:

24 ft up the wall

Step-by-step explanation:

We can use the Pythagorean theorem to solve, letting the 25 ft ladder be the hypotenuse

a^2 +b^2 = c^2

7^2 +b^2 = 25^2

49 + b^2 = 625

Subtract 49 from each side

49-49 +b^2 = 625-49

b^2 = 576

Take the square root of each side

sqrt(b^2) = sqrt(576)

b = 24

We only take the positive solution since length cannot be negative

The ladder will reach 24 ft up the wall

3 0

3 years ago

Evaluate the definite integral from pi/3 to pi/2 of (x+cosx) dx

Vadim26 [7]

Answer:

$\displaystyle \int\limits^{\frac{\pi}{2}}_{\frac{\pi}{3}} {(x + \cos x)} \, dx = \frac{5 \pi ^2}{72} + 1 - \frac{\sqrt{3}}{2}$

General Formulas and Concepts:

Calculus

Integration

Integrals

Integration Rule [Reverse Power Rule]: $\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C$

Integration Rule [Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)$

Integration Property [Addition/Subtraction]: $\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx$

Step-by-step explanation:

Step 1: Define

Identify.

$\displaystyle \int\limits^{\frac{\pi}{2}}_{\frac{\pi}{3}} {(x + \cos x)} \, dx$

Step 2: Integrate

[Integral] Rewrite [Integration Property - Addition/Subtraction]: $\displaystyle \int\limits^{\frac{\pi}{2}}_{\frac{\pi}{3}} {(x + \cos x)} \, dx = \int\limits^{\frac{\pi}{2}}_{\frac{\pi}{3}} {x} \, dx + \int\limits^{\frac{\pi}{2}}_{\frac{\pi}{3}} {\cos x} \, dx$
[Left Integral] Integration Rule [Reverse Power Rule]: $\displaystyle \int\limits^{\frac{\pi}{2}}_{\frac{\pi}{3}} {(x + \cos x)} \, dx = \frac{x^2}{2} \bigg| \limits^{\frac{\pi}{2}}_{\frac{\pi}{3}} + \int\limits^{\frac{\pi}{2}}_{\frac{\pi}{3}} {\cos x} \, dx$
[Right Integral] Trigonometric Integration: $\displaystyle \int\limits^{\frac{\pi}{2}}_{\frac{\pi}{3}} {(x + \cos x)} \, dx = \frac{x^2}{2} \bigg| \limits^{\frac{\pi}{2}}_{\frac{\pi}{3}} + \sin x \bigg| \limits^{\frac{\pi}{2}}_{\frac{\pi}{3}}$
Integration Rule [Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^{\frac{\pi}{2}}_{\frac{\pi}{3}} {(x + \cos x)} \, dx = \frac{5 \pi ^2}{72} + \bigg( 1 - \frac{\sqrt{3}}{2} \bigg)$

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

3 0

2 years ago

Read 2 more answers

1. Consider a cylinder with radius 4 cm and a height of 12 cm. Determine the volume of the given cylinder. Describe how to calcu

sergiy2304 [10]

↪Hola user_____________

⭐Here is Your Answer...!!!

____________________

↪SURFACE AREAS AND VOLUMES

↪The VOLUME of any object is nothing but the the capacity to hold the amount of substance inside it . It defines the Amount of substance that can occupied bythe object inside it ..

↪Volume = Base Area × Height

↪thus for the Cylinder ; Volume of cylinder = Pi(R^2) × H

↪thus volume = 3.14 × R^2 × H

↪thus here given as R = 4 cm and H = 12cm

↪Volume = 3.14 × 16 × 12= 602.88 cm^3

thus

↪the Volume of the Cylinder = 602.88 cm^3

______________________

⚓〽⭐

5 0

3 years ago

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you have an initial amount of 55$ in a savings account and you deposit an equal amount into your account each week. After 6 week

sveticcg [70]

55+added=133
added=amount addeed per week times 6=6x

55+6x=133
minus 55 both sides
6x=78
divide both sides by 6
x=13

add 13 per week

y=13x+55

3 0

3 years ago

Need help its 7th grade math

alexgriva [62]

Answer:

1 inch represents 60 feet.

Step-by-step explanation:

120/2

= 60

So his scale is 1:60

8 0

3 years ago

Read 2 more answers